Lower rank approximation of matrices by least squares with any choice of weights

Technometrics

Volumn 21, Issue 4, 1979, Pages 489-498

  Gabriel, K Ruben ^a   Zamir, S ^b  

^a UNIVERSITY OF ROCHESTER   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Biplot; Contingency table; Criss cross regression; Householder Young theorem; Least squares; Outliers; Reduced rank approximation

Indexed keywords

STATISTICAL METHODS;

EID: 0018546040     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1979.10489819     Document Type: Article

References (28)

1. BRADU, D. and GABRIEL, K. R. (1978). The biplot as a diagnostic tool for models of two-way tables. Technometrics, 20, 47-68.
2. CHRISTOFFERSON, A. (1969). The one-component model with incomplete data. Ph.D. Thesis, Uppsala University, Institute of Statistics.
3. FISHER, R. A. and MACKENZIE, W. A. (1923). Studies in crop variation. J. Agric. Sc., 13, 311-320.
4. GABRIEL, K. R. (1971). The biplot-graphic display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
5. GABRIEL, K. R. (1972). Analysis of meteorological data by means of canonical decomposition and biplots. J. App. Meteor., 11, 1071-1077.
6. GABRIEL, K. R. (1978). Least squares approximation of matrices by additive and multiplicative models. J. Roy. Statist. Soc., B, 40, 186-196.
7. GABRIEL, K. R. (1978). The complex correlational biplot. Theory Construction and Data Analysis in the Behavioral Sciences (S. Shye, ed.), pp. 350-370. San Francisco: Jossey-Bass.
8. GABRIEL, K. R. and BARAS, M. (1970). The Israeli rain- making experiment. Jerusalem: Hebrew University (mimeographed).
9. GABRIEL, K. R. and FEDER, P. (1969). On the distribution of statistics suitable for evaluating rainfall stimulation experiments. Technometrics, 11, 149-160.
10. GOOD, I. J. (1969). Some applications of the singular value decomposition of a matrix. Technometrics, 11, 823-831.
11. GOLUB, G. H. and PEREYRA, V. (1973). The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate. SIAM J. Numer. Anal, 10, 413-432.
12. GOLUB, G. H. and REINSCH, C. (1970). Singular value decomposition and least squares solution. Numer. Math., 14, 403-420.
13. HABER, M. and GABRIEL, K. R. (1977). Weighted least onical correlation and biplot display (mimeographed). Department of Statistics, University of Rochester.
14. HOUSEHOLDER, A. S. and YOUNG, G. (1938). Matrix approximation and latent roots. Am. Math. Monthly, 45, 165-171.
15. KESTER, N. K. (1979). Diagnosing and fitting concurrent and related models for two-way and higher-way layouts. Unpublished Ph.D. thesis, University of Rochester, Rochester, NY.
16. MANDEL, J. (1969). A method of fitting empirical surfaces to physical and chemical data. Technometrics, 11, 411-430.
17. MANDEL, J. (1971). A new analysis of variance model for non-additive data. Technometrics, 13, 1-18.
18. Mcneil, D. R. and TUKEY, J. W. (1975). Higher order diagnoses of two-way tables illustrated on two sets of demographic empirical distributions. Biometrics, 31, 487-510.
19. PLACKETT, R. L. (1962). A note on interactions in contingency tables. J. Roy. Statist. Soc., B, 24, 162-166.
20. ROY, S. N. (1957). Some Aspects of Multivariate Analysis. New York: Wiley.
21. ROY, S. N., GNANADESIKAN, R. and SRIVASTAVA, J. N. (1971). Analysis and Design of Certain Quantitative Multiresponse Experiments. Oxford: Pergamon.
22. RUHE, A. (1974). Numerical computation of principal components when several observations are missing. University of Umea, Institute of Mathematics and Statistics Report (mimeographed)
23. RUHE, A. and WEDIN, P. A. (1974). Algorithms for separable non-linear least squares problems. University of Umea, Institute of Mathematics and Statistics Report (mimeographed).
24. SCHWERTMAN, N. C. and ALLEN, D. M. (1973). The smoothing of an indefinite matrix with applications to growth curve analysis with missing observations. University of Kentucky, Department of Statistics, Technical Report No. 56 (mimeographed).
25. WHITTLE, P. (1952). On principal components and least square methods of factor analysis. Skand. Aktuar., 25, 232-239.
26. WISHART, D. (1978). Treatment of missing values in cluster analysis. Compstat 1978-Proceedings in Computational Statistics (L. C. A. Corsten and J. Hermans, eds.), pp. 281-287. Vienna: Physica-Verlag.
27. WOLD, H. and LYTTKENS, E. (1969). Nonlinear iterative partial least squares (NIPALS) estimation procedures. Bull. Inter. Statist. Inst., 43, 29-51.
28. WOLD, H. (1966). Nonlinear estimation by iterative least squares procedures. Research Papers in Statistics (F. N. David, ed.), pp. 411-444, New York: Wiley.